Basics of earth's radiation budget

As a result of a change in the state of energy, all matter greater than -273.15C (0K) radiates energy in the form of electromagnetic radiation following Stefan-Boltzmann's Law:

,

where &epsilon is emissivity (&epsilon =1 for a perfect blackbody, 0.95 < &epsilon < 0.98 for most other non-blackbody objects), &sigma is a constant equal to 5.67 10-8 W m-2K-4 , T is the temperature of the body in degrees centigrade, and E is the energy of the body given in units of W m-2. For example, for a blackbody body such as the sun with a skin temperature of 5600C, it's energy per unit area equals approximately 6.74 107 W m-2. The wavelength (in m) of maximum emission for any non 0K body is written as (Wien's Displacement Law):

,

thus, for example, the maximum emission wavelength of the sun is 4.9 10-1 m (490 nm).

The earth receives the electromagnetic radiation from the sun (typically defined as shortwave radiation) and emits it at longer wavelengths (typically defined as longwave radiation). Figure 1 depicts the earth's shortwave (blue lines) and longwave (red lines) energy fluxes.


Figure 1 Earth's energy budget (reproduced from Bonan, 2002)

The spectral component (i.e. radiation vs. wavelength) of the blackbody's emissive power can be computed using Planck's Law:

where I is the intensity of radiation (Wm-2sr-1) over an entire hemisphere, &lambda is wavelength (m), c is the speed of light (2.99 108 ms-1), h is Planck's constant (6.626 10-34 J s) and k is Boltzmann's constant (1.380658 10-23 Ws K-1).

Note: The aforementioned equation will output intensity as a function of wavelength in m. To determine the intensity as a function of wavelength at different wavelengths- say as nm- you must multiply the equation by the appropriate coefficient.


Figure 2 Hemispherical spectral emissive power for the emissions from the sun's surface (red line and y1-axis) and the earth's surface (green line and y2-axis). These graphs can be plotted using this gnuplot script and the Gnuplot freeware.

References:

Bonan, Gordon. 2002. Ecological Climatology: Concepts and applications. Cambridge Press, United Kingdom, 678 pp.

Siegel, Robert and Howell, John R. 1968. Thermal radiation heat transfer: Volume 1, the blackbody, electromagnetic theory, and material properties. Office of Technology Utilization, NASA, 190 pp.


Last Modified on Thursday, August 04, 2005 [an error occurred while processing this directive]